Here's one...

I picked up my new motor, 15hp yamaha 4-stroke, short shaft
It has manual tilt, so you click it up or down to adjust the angle of the motor.

Because the shaft is a bit longer than my old motor, I have to tilt it up to trailer it. Then of course it wants to bounce around. But you can't (at least I don't think you can) use a regular transom saver because you can't trim the motor down smoothly, its in increments. So how do you do this so the motor doesn't bounce around?

You can not disengage your motor lock so it freely moves up and down? My motor does not have tilt/trim and all I do is disengage the motor lock and let the motor come down till it sits in the transom saver then a bungee cord wich is attached to the transom saver is streched around the lower unit and cliped to the other side of the saver. If your motor does not have a way for it to disengage and freely move I do not know what to tell you but I would think it would.

Lotta ins, lotta outs, lotta what have-yous

When you disengage it, it does lower down smoothly. I didn't consider that you could have the transom saver on it while the tilt was not in one of its little notches. I'll see about finding one with the attachment for the roller on the trailer so it doesn't come off.

When I lower it I hold on to the lower unit so that it does not slam down into the saver. How is your Transom Saver attached to the trailer?

Lotta ins, lotta outs, lotta what have-yous

Don't really understand your problem (worked late and have'nt had my mug of coffee yet),I use a transom saver that I picked up from Cabela's for a 20hp short shaft and have no problem with it bouncin' around. Turn motor to either port or starboard side, put yolk of saver between fins of lower unit and secure with bungy cord that comes with unit. They can be purchased in different lengths and some adjustable to meet your needs ie., long-shaft, short-shaft, etc..
A transom saver in my book is a must, that engine will put a lot of stress on your transom (sure your aware of that)especially with it bouncin'. Don't know if this novel helped ya', but hope you resolve the problem. Have a good one. Outta here... ~Skip